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There is no assurance that interface states can be found at the boundaryseparating two materials. As a strong perturbation typically favors wavelocalization, it is natural to expect that an interface state should form moreeasily in the boundary that represents a strong perturbation. Here, we show onthe contrary that in some two dimensional photonic crystals (PCs) with a squarelattice possessing Dirac-like cone at k=0, a small perturbation guarantees theexistence of interface states. More specifically, we find that single-modelocalized states exist in a deterministic manner at an interface formed by twoPCs each with system parameters slightly perturbed from the conical dispersioncondition. The conical dispersion guarantees the existence of gaps in theprojected band structure which allows interface states to form and the assuredexistence of interface states stems from the geometric phases of the bulkbands.

Deterministic formation of interface states in some two-dimensional photonic crystals with conical dispersions